Drag each statement to show whether it is true, based on the graph.

As all the length of each side of given triangle are unequal so the given triangle is scalene triangle

A triangle's perimeter is defined as the total length of its boundary.

The perimeter of a triangle is the sum of all three sides.

Here given that there is a triangle name ABC and the triangle ABC has the perimeter of 90.

∴ Sum of sides of triangle ABC will equal to the perimeter of triangle ABC

∴ AB + BC + AC = 90

As we have AB = 5x + 1, BC = 2x + 13, AC = x + 4

∴ 5x + 1 +  2x + 13 + x + 4 = 90

∴ 8x + 18 = 90

∴ 8x = 90 - 18

∴ 8x = 72

∴ x = 72/8

∴ x = 9.

So we get AB = 5x + 1 = 5(9) + 1 =45 + 1 = 46.

BC = 2x + 13 = 2(9) + 13 = 18 + 13 = 31.

AC = x + 4 = 9 + 4 = 13.

As all the length of each side are unequal so the given triangle is scalene triangle as an scalene triangle is a triangle in which all three side lengths are different and all three angle measurements are different. However, the sum of all interior angles is always equal to 180 degrees. Therefore, it satisfies the angle sum property of triangles.

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The probability of getting an even number is 1/2 while the probability of getting a factor of 6 is 1/6

The probability of an even number

From the question, the sample space of the number cube is given as

Space = 1, 2, 3, 4, 5, and 6

The above means that

Sample size, n = 6 ---- i.e. the number of observations

Number of even numbers, x = 3

The probability of getting an even number is then calculated as

P(Even) = Number of even numbers/Sample size

This gives

P(Even) = 3/6 = 1/2

The probability of a factor of 6

From the question, the sample space of the number cube is given as

Space = 1, 2, 3, 4, 5, and 6

The above means that

Sample size, n = 6 ---- i.e. the number of observations

Number of factor of 6, x = 1

The probability of getting a factor of 6 is then calculated as

P(factor) = Number of factor of 6/Sample size

This gives

P(factor) = 1/6

Hence, the probability is 1/2 and 1/6

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The estimated standard deviation from the range rule is 145.5 cm3.As it is 29.8 cm3 smaller than the exact standard deviation, we consider that the estimation is not accurate enough.

Generally, brain volumes which are smaller than 921.1 cm3 can be considered significantly low and bigger than 1417.5 cm3 can be considered significantly high. Hence, brain volume of 1457.5 cm3 is bigger than the expected maximum, so it can be considered significantly high.

The calculation goes like this,

According to the range rule, the standard deviation and range, or the distance between the maximum and smallest value, are roughly inversely proportional:

[tex]s=R/4[/tex]

If we have a sample of 50 brains volumes, and they range from 910 cm3 to 1492 cm3, we can estimate the standard deviation as:

[tex]s=max-min/4[/tex]

s=1492-910/4=582/4=145.5

The exact standard deviation is 175.3 cm3.The difference is 175.3-145.5=29.8 cm3, so the estimation is not accurate enough.

The range rule of thumb states that we should anticipate a maximum value that is approximately two standard deviations above the mean and a lowest value that is approximately two standard deviations below the mean. The expected ranges are as follows given our mean volume of 1169.3 cm3 and standard deviation of 124.1 cm3:

Min= M-2s=1169.3-2*124.1=921.1

Max=M+2s=1169.3+2*124.1=1417.5

The brain capacity of 1457.5 cm3 can be regarded as significantly high because it is higher than the predicted maximum.

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Answer: k>8.14

Step-by-step explanation: just do math.

The equation of the parabola will be;

y = (x - 3)² + 1

What is mean by Parabola?

A parabola is a set of points in the plane which are equidistant from the directrix and focus.

Given that;

The vertex of the parabola = (3 , 1)

A parabola passes through the point (2,2).

Now,

Since, The equation of parabola in vertex form is;

y = a (x - h)² + k

Where, (h , k) are vertex of the parabola.

So, The equation of parabola with vertex (3, 1) will be;

y = a (x - 3)² + 1

And, It passes through the point (2,2).

So we substitute the value of (2, 2) in place of (x, y) as;

2 = a (2 - 3)² + 1

2 = a + 1

a = 2 - 1

a = 1

Substitute the value of a in above equation, we get;

The equation of parabola as;

y = (x - 3)² + 1

Therefore, The equation of the parabola will be;

y = (x - 3)² + 1

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System of inequalities are :

y> [tex]x^{2} -4[/tex] and y > [tex]x^{2} +3[/tex]

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With the concepts of percentages and calculations, the percent decrease in the number of people who went to the pool over these four weeks is 10%

Take the base as 100 and convert the percentage to numbers and then proceed with the same.

Now, the initial number of people in the local swimming pool is 1020, after which 100 fewer went, hence 920 people

Now, 135 people more people need to be added, thus 1055 people.

Now, 137 fewer people went, so 918 people went to the pool in the four weeks.

Therefore percent decrease = Difference/No. of people in the first week * 100

Thus, the percent decrease =  102/1020*100=10%

Hence 10% of people went less in the fourth week as compared to the first week.

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[10] D

      A counter-example is an example that shows the argument can have true premises and a false conclusion.

      Option D shows someone who is good at math, but isn't an engineer. This is a counter-example.

[11] B

      Similar to the previous question, options A, B, and D are all dogs. However, option C is not a dog and also has four legs. Therefore, it is a counter-example.

The given inequality is,

The graph of the inequality will be shown below

Answer:

I believe it's " a study that collects data on every subject in sample"

Step-by-step explanation:

1.work out area of a single plot

[tex]area = 9 \times 7[/tex]

[tex]area = 63m ^{2} [/tex]

2.multiply the area by the amount of workers

[tex]total \: area = 63 \times 3[/tex]

[tex]total \: area \: = 189m ^{2} [/tex]

Answer:

Slope is -2!

y= -2x

Step-by-step explanation:

Based on the 2 points given: (3, -6) (-3, 6)

The tunnel measures 225 meters in length.

Velocity is the measure of how quickly an object's position changes over time and in relation to a frame of reference. A body moves across space with uniform velocity when it does so with an equal displacement per unit of time.

Velocity is equal to the product of distance and time.

It measures in m/s.

In response to the query, we are provided with the-

150m is the length of the train.

s m is the tunnel's length.

90 km/hr is the train's speed.

= 90 × 5/18 m/sec

= 25m/sec

Total distance equals (train length plus tunnel length).

[tex]Speed = \frac{Distance}{Time}[/tex]

⇒ 25 = (150 + s) / 15

⇒ 25 × 15 = 150 +s

⇒ 375 = 150 + s

⇒ 375 - 150 = s

⇒ s = 225

⇒ s = 225m

Hence, the length of the tunnel is 225 m.

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Answer:

2

Step-by-step explanation:

So to get the answer we need to figure out what x is

2×2=4

so x has to be 2

Answer:

y = 6.75x

Step-by-step explanation:

$33.75 ÷ 5 = $6.75

$47.25 ÷ 7 = $6.75

So we have y = 6.75x.

Answer:

See below

Step-by-step explanation:

[tex]\frac{1}{a+b}[/tex] ([tex]\frac{1}{a}[/tex] + [tex]\frac{1}{b}[/tex])

[tex]\frac{1}{a+b}[/tex] ([tex]\frac{b}{ab}[/tex] + [tex]\frac{a}{ab}[/tex])

[tex]\frac{1}{a+b}[/tex] ([tex]\frac{b+a}{ab}[/tex])

[tex]\frac{(a+b)}{(a+b)(ab)}[/tex]

[tex]\frac{1}{ab}[/tex]

[tex]ab^{-1}[/tex]

The result of the expression 3x-(2x+10) for x = [tex]7\frac{5}{13}[/tex] is -2.61

The expression is

3x-(2x+10)

The expression is the mathematical sentence with a minimum of two variables and at least one math operation.

The value of the x = [tex]7\frac{5}{13}[/tex]

Convert the mixed fraction to the simple fraction

[tex]7\frac{5}{13}[/tex] = 96/13

Convert the simple fraction to the decimal form

96/13 = 7.39

Substitute the value of x in the given expression 3x - (2x + 10)

= 3 × 7.39 - (2×7.39 + 10)

Multiply the terms first

= 22.17 - (14.78 + 10)

= 22.17 - (24.78)

= -2.61

Hence, the result of the expression 3x-(2x+10) for x = [tex]7\frac{5}{13}[/tex] is -2.61

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Answer:

The well-desgined graph has an appropriate scale for the y-axis. By appropriate we mean that the scale is such that all points on the graph can be discerned easily. In other words, the scale is not too wide or too narrow.

For graph A, the scale is such that the data points are at such a distance from each other that their values can be easily read off. On the other hand, for graph B, there isn't enough vertical distance between the data points for them to be easily read.

Answer:

True

Step-by-step explanation:

Matching sides of two or more polygons are titled corresponding sides,and matching angles are titled corresponding angles . If two figures are lookalike,then the measures of the corresponding angles are similar and the ratios of the lengths of the corresponding sides are proportional .

Answer:

5/6

Step-by-step explanation:

Step 1: Find the GCD (greatest common denominator)

12

Step 2: multiply your factions to represent this

[tex]\frac{2x3}{4x3} = \frac{6}{12} \\[/tex] , [tex]\frac{1x4}{3x4} = \frac{4}{12}[/tex]

Step 3: add the numerators:

[tex]\frac{6}{12} + \frac{4}{12} = \frac{10}{12}[/tex]

Step 4: reduce your fraction

[tex]\frac{10}{12} = \frac{5}{6}[/tex]

Hope that helps

Fraction multiplication

2/4 x 1/3

We reduce the fraction 2/4 to its lowest expression by extracting and canceling 2.

1/2 x (1/3)

Multiply 1/2 by 1/3 (to do this, multiply the numerator by the numerator and the denominator by the denominator).

1 x 1/2 x 3 =====> Multiply

1/6  ====> Answer

The balance on his credit card will be the amount of $4076.56 one year from now.

Simple interest is defined as interest paid on the original principal and calculated with the following formula:

S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100

First, we must compute James' monthly charges on his balance of 4289.

Principal = 4289

Rate = 5%

Time = 1 month = 1/12 year

Simple interest = 4289×5×1/12×100 = 17.87

The monthly charge is 17.87,

So the yearly charge would be: 12 × 17.87 = $214.44

His credit card balance one year from now = Principal - Interest

⇒ 4289 - 214.44

⇒ 4076.56

In one year, his credit card amount will be 4076.56.

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the coordinates of point c is (9/2, -3/2)

The original coordinate = C(6, -2)

scale factor r =3/4

New coordinate (c) = scale factor × the original coordinate

c = 3/4(6, -2)

c = (3/4×6, -2×3/4)

c = (18/4, -6/4)

c = (9/2, -3/2)

Hence, the coordinates of point c is (9/2, -3/2)

Answer:

  18

Step-by-step explanation:

You want to know the number of pencils in a box when 7 more than 4 boxes totals 79 pencils.

Let b represent the number of pencils in a box. Then the total number of pencils Mr. Ridley has is ...

  4b +7 = 79

This 2-step linear equation is solved in the usual way:

Step 1: isolate the variable term

  4b +7 -7 = 79 -7 . . . . . . add the opposite of the left-side constant

  4b = 72 . . . . . . . . . simplify

Step 2: isolate the variable

  4b/4 = 72/4 . . . . . . . . . . divide by the coefficient of the variable

  b = 18 . . . . . . . . . . simplify

There were 18 pencils in each of Mr. Ridley's pencil boxes.

Answer:

130 miles

Step-by-step explanation:

65×2=130 So if I am driving at a rate of 65 mph then in one hour I drive 65 miles. Since it is in 2 hours I will have driven 130 miles.

Answer:

130 miles.

Step-by-step explanation:

so it said that the car is traveling 65 miles per hour and it wants to know how far it would go in 2 hours. so if 1 hour is 65 miles if we multiply it by two then we will get

65 miles = 1 hour

130 miles = 2 hours

Answer:

a) 81

b) 16807

c) 1010000000

d) 390630

These are all correct. I checked.

The slopes for each couple of points are summarized below:

Geometrically speaking, slopes in lines indicates the grade of steepness of the line itself. The slope of the line can be determine by knowning the coordinates of two distinct points set on Cartesian plane and using the secant line formula, whose definition is shown below:

m = Δy / Δx

Where:

Now we proceed to answer on each case:

Case 1

m = [3 - (- 1)] / [3 - (- 3)]

m = 4 / 6

m = 2 / 3

Case 2

m = (- 2 - 1) / [2 - (- 2)]

m = - 3 / 4

Case 3

m = [2 - (- 4)] / [- 4 - (- 1)]

m = 6 / (- 3)

m = - 2

Case 4

m = Undefined, as Δx = 0.

Case 5

m = [3 - (- 1)] / (3 - 2)

m = 4

Case 6

m = 0, as Δy = 0

Case 7

m = (6 - 9) / (1 - 4)

m = - 3 / (- 3)

m = 1

Case 8

m = [- 5 - (- 1)] / [- 2 - (- 4)]

m = - 4 / 2

m = - 2

Case 9

m = (- 9 - 3) / (5 - 5)

m = - 12 / 0

m = Undefined

Case 10

m = (9 - 1) / (8 - 2)

m = 8 / 6

m = 4 / 3

Case 11

m = [- 6 - (- 8)] / (7 - 14)

m = 2 / (- 7)

m = - 2 / 7

Case 12

m = [- 3 - (- 3)] / (8 - 4)

m = 0 / 4

m = 0

Case 13

[8 - (- 4)] / (2 - x) = - 3

12 = - 3 · (2 - x)

12 = - 6 + 3 · x

18 = 3 · x

x = 6

Case 14

(4 - y) / (3 - 10) = - 2 / 7

(4 - y) / (- 7) = - 2 / 7

4 - y = - 2

y = 6

Case 15

(4 - 1) / (x - 7) = 3 / 4

3 / (x - 7) = 3 / 4

x - 7 = 4

x = 11

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Answer:

I will assume that 2√√/2 is actually 2[tex]\sqrt{2}[/tex]

Vab = 8

Step-by-step explanation:

ab

([tex]\sqrt{8}[/tex])*( 2[tex]\sqrt{2}[/tex])

2*[tex]\sqrt{16}[/tex]

2*4

Vab = 8